Random Walk in a Finite Directed Graph Subject to a Road Coloring

A necessary and sufficient condition for a random walk in a finite directed graph subject to a road coloring to be measurable with respect to the driving process is proved to be that the road coloring is synchronizing. The key to the proof is to find a hidden symmetry in the non-synchronizing case.

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Bibliographic Details
Published inJournal of theoretical probability Vol. 26; no. 1; pp. 259 - 283
Main Author Yano, Kouji
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.03.2013
Subjects
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Statistics
60J10
Stochastic difference equation
Random walk on directed graph
60B15
Road coloring
05C81
37H10
Strong solution
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Summary:A necessary and sufficient condition for a random walk in a finite directed graph subject to a road coloring to be measurable with respect to the driving process is proved to be that the road coloring is synchronizing. The key to the proof is to find a hidden symmetry in the non-synchronizing case.
ISSN:0894-9840
1572-9230
DOI:10.1007/s10959-011-0398-8